Some Mathieu-type series for generalized H-function associated with a certain class of Feynman integrals

Abstract

Closed form expressions are investigated for a family of convergent Mathieu type a-series and its alternating variant, whose terms contain a generalized H-function associated with certain Feynman integrals. The results derived are of general character and provide an elegant generalization for the closed form expressions of these series associated with the H-function by Pogány [Integral expressions of Mathieu-type series whose terms contain Fox's H-function, Appl. Math. Lett. 20 (2007), pp. 764–769], for Fox–Wright Ψ-functions by Pogány and Srivastava [Some Mathieu-type series associated with the Fox–Wright function, Comput. Math. Appl. 57 (1) (2009), pp. 127–140] and for _p F _q and Meijer's G-function by Pogány and Tomovski [On Mathieu-type series which terms contain generalized hypergeometric function _p F _q and Meijer's G-function, Math. Comput. Modell. 47 (9–10) (2008), pp. 952–969], and others.

Keywords:

• H¯-function
• H-function
• Fox–Wright Ψ-function
• Generalized Zeta function
• Mathieu a-series
• Feynman integrals

2000 AMS Subject Classification :

• primary 33C20
• 33C60
• secondary 40G99
• 44A20

Acknowledgements

The work of the first author was supported in part by Research Project No. 112- 2352818-2814 of Ministry of Science, Education and Sports of Croatia. Both the authors would like to thank the Associate Editor Professor H. M. Srivastava and the referee for carefully reading the paper and for their valuable comments and useful suggestions.